A11705. Circles of Waiting

A chip was placed on a field with coordinate system onto point $(0,0)$ .

Every second the chip moves randomly. If the chip is currently at a point $(x,y)$ , after a second it moves to the point $(x-1,y)$ with probability $p_{1}$ , to the point $(x,y-1)$ with probability $p_{2}$ , to the point $(x+1,y)$ with probability $p_{3}$ and to the point $(x,y+1)$ with probability $p_{4}$ . It's guaranteed that $p_{1}+p_{2}+p_{3}+p_{4}=1$ . The moves are independent.

Find out the expected time after which chip will move away from origin at a distance greater than $R$ (i.e.  will be satisfied).

First line contains five integers $R,a_{1},a_{2},a_{3}$ and $a_{4}$ ( $0<=R<=50,1<=a_{1},a_{2},a_{3},a_{4}<=1000$ ).

Probabilities $p_{i}$ can be calculated using formula .

It can be shown that answer for this problem is always a rational number of form , where .

Print $P·Q^{-1}$ modulo $10^{9}+7$ .

In the first example initially the chip is located at a distance $0$ from origin. In one second chip will move to distance $1$ is some direction, so distance to origin will become $1$ .

Answers to the second and the third tests:  and .